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\author{Piyush P Kurur\\
  Office no: 224\\
  Dept. of Comp. Sci. and Engg.\\
  IIT Kanpur}


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\title{Fundamentals of Computing: Lecture 9}
\date{August 17, 2009}
\begin{document}
\begin{frame}
\maketitle
\end{frame}

\begin{frame}
  \frametitle{Summary of last class}
  \pause
  \begin{itemize}
  \item We looked at the tower of hanoi problem.
    \pause
  \item We gave a recursive solution to that problem.
    \pause
  \end{itemize}
\end{frame}

\begin{frame}
  \begin{block}{Another example}
    Given an integer $n$ print the sequence
    $n, n-1,\dots,1, 0, 1, \ldots, n - 1, n$
  \end{block}
\end{frame}
\begin{frame}
  \begin{block}{Using iteration}
    \begin{code}
      # include<stdio.h>
      void downUp(int n)
      {
        for(int i = n; i > 0; i--)
        {
          printf("%d, ", i);
        }
        printf("0");
        for(int i = 1; i <= n; i ++)
        {
          printf(", %d", i);
        }
      }
    \end{code}
  \end{block}
\end{frame}

\begin{frame}
  Let $S_n$ denote the sequence $n,\ldots, 0 , \ldots, n$.
   \begin{block}{Recursive definition}
    \begin{eqnarray*}
      S_{0} & = &  0\\
      S_{n} & = & n, S_{n-1}, n
    \end{eqnarray*}
  \end{block}
  \pause
  \begin{code}
    void downUpRec(int n)
    {
      if(n <= 0) 
      {
        printf("0");
        return;
      }
      printf("%d, ", n); 
      downUpRec(n-1);
      printf(", %d", n);
    }
  \end{code}
\end{frame}

\begin{frame}
\begin{block}{The |main| function}
  \begin{code}
    void downUpRec(int);
    void downUp(int );

    int main()
    { 
      int n;
      printf("enter the number: ");
      scanf("%d",&n);
      printf("Iterative:\t");
      downUp(n);
      printf("\nRecursive:\t");
      downUpRec(n);
      printf("\n");
    }
  \end{code}
\end{block}
\end{frame}
\begin{frame}
  \frametitle{Separate compilation}
  \begin{itemize}
  \item Create a file |downUp.c| that contains the 
    definition of the function |void downUp(int)|
  \item Create a file |downUpRec.c| that contains the
    definition of the function |void downUpRec(int)|
  \item Create a file |main.c|
  \end{itemize}
  
  \begin{block}{Compiling}
    \begin{spec}
      $ gcc -std=c99 main.c downUp.c downUpRec.c
      $ gcc -std=c99 -c downUp.c
      $ gcc -std=c99 -c downUpRec.c
      $ gcc -std=c99 main.c downUp.o downUpRec.o
    \end{spec}
  \end{block}
\end{frame}
\end{document}